Including Nanoscale Investigations in Undergraduate Physics Laboratories at all Levels of the Curriculum

Transcription

1 Mater. Res. Soc. Symp. Proc. Vol Materials Research Society 0931-KK03-02 Including Nanoscale Investigations in Undergraduate Physics Laboratories at all Levels of the Curriculum Kurt Vandervoort, Asif Hyder, Stephanie Barker, and Raul Torrico Physics Dept., California State Polytechnic University, Pomona, CA, ABSTRACT A series of laboratory modules were developed to introduce atomic force microscope (AFM) applications into undergraduate physics courses. The goal is to elucidate fundamental physics concepts at the nanoscale that will complement existing investigations at the macroscale, and to expose students to advanced instrumentation at an early level. The experiments allow students to experience the full range of scanning probe modes available, which include contact, intermittent contact, lateral force, and magnetic force microscopy as well as force distance spectroscopy. The course levels span the range from freshman introductory to advanced senior level and allow students to experience AFM applications at successive levels of complexity. INTRODUCTION A series of nanotechnology modules were developed at California State Polytechnic University with support from the NSF-NUE (National Science Foundation - Nanotechnology Undergraduate Education) program. These nanoscale modules were primarily developed for freshman- and sophomore-level physics service courses to supplement existing experiments of macroscale phenomenon. In addition, these introductory modules were modified for more advanced level experiments for placement in our upper-level physics courses. The goals behind these curricular changes were to (1) introduce students to research grade instrumentation at an early level that they may likely encounter in their future careers or in graduate school; (2) create a hierarchy of courses, where students are introduced to advanced instrumentation and experimental techniques at successive stages of complexity from freshman to senior level; and (3) provide cross-disciplinary activities that demonstrate the utility and relevance of physics for majors in other disciplines. This last goal is consistent with the findings of others [1, 2], in science education research, who emphasize the importance of cross-disciplinary diversity for undergraduates as necessary preparation for the current employment market. EXPERIMENTAL DETAILS The atomic force microscope used in all module development was a Quesant Instruments Universal Scanning Probe Microscope. Commercial silicon cantilevers from MikroMasch TM were employed with resonant frequencies from khz and spring constants from N/m for contact mode and from khz and from N/m for intermittent contact mode. Magnetic Force Microscope cantilevers from Nano Sensors TM were employed with resonant frequencies from khz and spring constants from N/m. The scanning head portion of the microscope was placed on a vibration isolation platform (BM-4 platform from Minus K Technology) to limit influences from floor vibrations and this platform was placed in a chamber

2 (Novascan) to limit influences from acoustic vibrations. To facilitate ease in transport to the various physics laboratories, the chamber was placed on a table fitted with rolling casters. DISCUSSION Modules were developed for each quarter of the four-quarter introductory calculus-based physics sequence. In addition, these modules were adapted for use in the three-quarter algebrabased physics sequence and for upper level physics laboratories. In all, eight primary modules were developed and are described below. Nanoscale Measurements module One of the first experiments students perform in the introductory physics sequence is an experiment that focuses on measurements and uncertainty. Students measure the volumes and masses of various shaped objects using rulers, calipers and mass balances and then calculate the densities of these objects with their propagated uncertainties. For objects of the same material, for example copper, students compare their calculated densities to see if they match within the uncertainty of their measurements. To expose students to a much wider range of length scales, we include a supplement to this lab that includes measurements at the nanoscale. Students image a compact disk (CD) using the AFM in contact mode over a scan area of 5 X 5 µm 2 (see figure 1). They then observe a cross section of this image to determine the approximate dimensions of the bumps and answer questions concerning comparisons between the size of the bumps, the size of an atom and the size of a human hair. They ultimately determine the approximate number of bumps that could fit on an entire CD and obtain a value of the same order of magnitude as the storage capacity of a typical CD, ~700 megabytes. In a follow up exercise, students observe an atomic scale image (obtained by others and downloaded from a website) of the surface of copper obtained by a scanning tunneling microscope in ultrahigh vacuum. They are asked to count the number of copper atoms along a 3- nm line superimposed on the image and, from this measurement and the atomic mass of copper, determine copper's density. For the sake of simplicity consistent with the level of the course, they are told to assume a simple cubic structure in their calculations and obtain a value for the density that is not accurate but of the same order of magnitude as from their macroscopic measurements. The activities provided in the nanoscale supplement reveal to the students the wide range of length scales available to present day and future technology. In addition, students gain important practice in unit conversions over several orders of magnitude.

3 Figure 1. Three-dimensional, 5 X 5 µm 2 AFM image of a non-recordable compact disk. To obtain this image, one must use a razor blade to scrape off the top paper-coated layer of the CD and image the reflective underside. Nanoscale Friction module In an introductory mechanics experiment, students measure the acceleration of masses on an Atwood machine and graph the net external force on the system versus the acceleration. Their graphs yield a y intercept, which is linked to the frictional force on the pulley. To examine friction on a microscopic scale, students image the surface of highly oriented pyrolytic graphite (HOPG) using the AFM. They scan a 1 square micron area of a freshly cleaved surface in contact mode. HOPG is of near single-crystal quality and is atomically flat over most of its surface. Defects on the surface are easily discernable and normally consist of monolayer steps. Students readily observe these defects in the topographic image. Along with the surface topography data, the AFM stores data for the lateral forces (forces parallel to the surface) exerted on the tip as it scans. These lateral forces are associated with friction and students can easily access this frictional image and compare it to the image of the surface topography. While most of the features in the frictional force image correspond to changes in surface topography, there are some that do not. For example, there are significant frictional forces associated with impurities on the surface from contamination, which can become more prominent with time. In addition, there is a measurable non-zero frictional force over the atomically flat regions. Students answer questions dealing with these issues that help to increase their awareness of friction as a complex phenomenon. The experiment serves to expand student perceptions of the origins of friction as more than solely a consequence of surface irregularities. Electrostatics module In one of the first experiments in electricity and magnetism, students investigate electric fields between various charge distributions by mapping equipotential lines on conducting paper. To complement these investigations, we have inserted a supplement to the existing experiment

4 that uses the AFM in force spectroscopy mode, to examine the attractive and repulsive forces between the AFM tip and a gold surface. In force spectroscopy mode, the tip is brought into and away from the surface as the normal force on the tip is recorded (see figure 2). Students record the maximum repulsive and attractive forces from the data and compare these nanoscale forces to more readily discernable forces, for example, the weight of an ant. They are also asked to speculate as to the electrostatic origin of both the attractive and repulsive forces. The experiment serves to increase student awareness of the complexities associated with interatomic forces. In addition, it demonstrates that charge configurations with zero net charge may exhibit both attractive and repulsive interactions, due to polarization or due even to quantum effects, such as overlapping electron clouds. 200 Tip Approaching Force (nn) Tip Withdrawing Distance (nm) Figure 2. Example force-spectroscopy curve. The force represents the force measured on the AFM tip and the distance represents the distance traveled by the tip as it is brought into the gold surface from its initial (zero) position above the surface. Magnetic Fields module In one of the last experiments in electricity and magnetism, students investigate the magnetic field profile of a long solenoid and a short coil. To demonstrate the variation of magnetic fields on the nanoscale, a module was developed to image the magnetic domains on a zip disk. For this application, the AFM was used in magnetic force mode. A special cantilever, with a ferromagnetic tip, is used and the tip is first polarized by a strong, rare-earth magnet. A small piece of the zip disk, fastened to a glass slide, is imaged in topology-amplitude mode by the AFM. In this mode, the tip oscillates as in intermittent contact mode and the oscillation amplitude is monitored. For each scan line, the tip first performs a standard surface measurement at a close distance to sample, where short-range interatomic forces overwhelm the long-range magnetic forces. From this scan, the topography of the surface is determined. The tip then moves upward to some predetermined height (where the long-range magnetic forces dominate the short-range interatomic forces) and repeats a scan moving up and down with the premeasured contours of the surface. The software computes the difference between the two scans to determine the forces that are magnetic in origin.

5 As shown in figure 3, the zip disk image contains magnetic domains with widths of about 1.5 microns and lengths of about 10 microns. From these results, students are able to determine the area associated with one bit of digital information (one domain), and from the radius of a disk, 4.5 cm, the total storage area available. Their calculation yields 400 megabytes of nominal storage capacity, close to the designated capacity of the disk, 250 megabytes. The 400 megabyte maximum capacity calculation seems reasonable, since much of the available space is used for purposes other than data storage, e. g. servo information such as data sector number, track number and information for centering the head on the track. Figure 3. AFM (in magnetic force mode) top-view image of a zip disk. Geometric Optics module Students are first introduced to geometrical optics in an experiment that investigates images produced by lenses. Much of their analysis involves ray-tracing diagrams, where light is assumed to reflect and refract in straight-line paths. We have inserted a supplement to this lab that demonstrates the physical criteria that define the limits for the ray approximation. A smooth glass slide and rough glass slide were sputtered with equivalent thicknesses of gold. As shown in figure 4, students can readily attest to the specular reflective properties of the smooth slide and the diffuse reflective properties of the rough slide. Upon closer examination of these surfaces with the AFM, the criteria delineating these two reflective regimes is revealed. Cross sections of the AFM images show that the average size of the largest features on the specularly reflective surface (see figure 5) is significantly less than the wavelengths of visible light while the average size of the largest features on the diffuse reflective surface (see figure 6) is significantly greater than the wavelengths of visible light. The experiment reveals the microscopic origin of the properties of light-surface interactions in a straightforward manner.

6 Figure 4. Rough glass slide (left) and smooth glass slide (right) sputtered with gold. Figure 5. Cross section of AFM image of smooth glass slide sputtered with gold. Average size (height variation) of largest surface features is ~ 10 nm, significantly less than the wavelengths of visible light. Figure 6. Cross section of AFM image of rough glass slide sputtered with gold. Average size (height variation) of largest surface features is ~ 2000 nm, significantly greater than the wavelengths of visible light. Physical Optics module The physical optics lab follows the geometric optics lab and involves measurements of patterns produced by single- and multiple-slit interference. For this experiment, we have

7 inserted an AFM supplement where students determine the origin of the rainbow reflective properties of a compact disk, a property that they are readily familiar with. As shown in figure 7, for this measurement, a significantly larger scan area is imaged on the CD than was imaged for the Nanoscale Measurements module, so that the average distance between the rows of bumps could be determined. The value students obtain for the row spacing is approximately 1600 nm. As a macroscopic verification of this value, students then treat the CD as a reflective diffraction grating and shine light from the same helium-neon laser as they used in the single-slit and multiple-slit portion of the lab. They measure the angles of the two first-order interference peaks, and calculate the row spacing using the standard Fraunhofer interference equation. Their two values for the row spacing are usually within 5% of one another. Figure 7. Three-dimensional, 20 X 20 µm 2 AFM image of a non-recordable compact disk. Image obtained in the same manner as prescribed for figure 1. Spectroscopy module In a practical application of physical optics, students investigate the spectrum of hydrogen. They use a spectrometer with a diffraction grating and a telescope to view and measure the precise angles for the first- and second-order interference lines of the spectrum. They then calculate the wavelengths of these lines using their measured angles and the stated spacing of the grooves on the diffraction grating. In the new supplement to this experiment, students image the surface of the diffraction grating using the AFM and verify the groove spacing that is stamped on the side of the grating. In addition, the AFM image (see figure 8) reveals the surface geometry, which is probably different than student perceptions of the grating, as a flat surface with a series of slits. The geometry of the surface is important in terms of the angle of the grooves, also known as the blaze angle. In the follow up experiment to the spectroscopy lab, the students investigate the purpose of the blaze angle in more detail, as described below in the Microwave Optics module.

8 Figure 8. Three-dimensional, 5 X 5 µm 2 AFM image of a transmission diffraction grating. Microwave Optics module The microwave optics experiment allows students to investigate the properties of electromagnetic radiation on length scales of a few centimeters. Students examine many properties of microwaves, including polarization, reflection, refraction and one- and two-slit interference. We have included a supplement to the existing experiment to investigate the purpose of the blaze angle of a diffraction grating that the students observed in their previous week s lab on spectroscopy. From the spectroscopy experiment, students encounter the reduced intensity of the higherorder spectral lines, that is, the less intense second-order compared to the first-order. The origin of this reduced intensity is from the diffraction envelope of the pattern, which is dependent on the width of the grooves. Gratings are often blazed [3] so that the center of the diffraction envelope (where the intensity is highest) is shifted from its normal location, at the center of the interference pattern (zeroth order maximum), to any desired higher order interference maxima. Since all wavelengths exhibit an interference peak at the same zeroth order maximum position, higher intensity at this position is undesirable and shifting the center of the diffraction envelope to higher order maxima, where different wavelengths are separated, is the goal. Students perform the microwave experiment using standard physics education equipment [4] for a two-slit interference pattern with and without a blazed macroscopic diffraction grating, as shown in figure 9. The diffraction grating (see figure 10) is 10-cm thick and made from four equivalent machined pieces of one-inch thick Plexiglas, glued together with clear epoxy. Figure 11 displays the microwave intensity as a function of angle for the two-slit interference pattern with and without the diffraction grating. The original two-slit pattern demonstrates the strong attenuation of the first order peaks as compared to the central maximum which emphasizes the need to shift the diffraction envelope. The pattern with the diffraction grating demonstrates the shift of intensity away from the central maximum and to the first order maximum near -29 º. In addition, the intensities of the central maximum and maximum at +29 º are correspondingly attenuated. The experiment provides a way for students to easily visualize the purpose of the blaze angle and exposes them to an interesting engineering application. Significant further details for this module can be found elsewhere [5].

9 0 T θ R + Plates Grating Figure 9. Microwave experiment with transmitter (T), receiver (R), reflector plates and diffraction grating. Distances are not to scale. Figure 10. Plexiglas (macroscopic) diffraction grating. Relative Intensity Angle (degrees) Figure 11. Data for the two-slit interference experiment with (solid circles) and without (open circles) the diffraction grating. The total integrated intensity over all angles for the data without the diffraction grating is greater than with the grating due to the less than 100% transmittance of microwaves through the Plexiglas.

10 Adaptation to upper level courses Several adaptations of these primary modules were made so that they could be included as stand-alone experiments in our upper level courses. For example, more detailed investigations of the topography of a CD surface have been developed into a senior level lab. An enormous amount of thought has gone into the engineering of a CD, and the size, orientation and distance between the bumps has been precisely designed [6]. For example, the height of these bumps is an important parameter for the proper operation of the CD. Students measure a series of bumps and obtain an average for their height. They are supplied with information about the wavelength of the laser light used in a CD, 780 nm, and then use this information and their measured bump height to determine the index of refraction of the polycarbonate material on top of the bumps. The calculation involves the knowledge that the interaction of the laser with a bump and surrounding area requires destructive interference, so that the height of the bumps is precisely 1/4 of the wavelength of the laser light in the polycarbonate material. The students calculate indices of refraction that are typically within 10% of stated values from the manufacturer. The Spectroscopy module was modified to include more detailed analysis of the blaze angle. For a transmission diffraction grating that is blazed to shift the center of the diffraction envelope to one of the first-order interference maxima, the relationship between the index of refraction of the glass, n, the blaze angle θ B, and the first-order interference angle, θ 1, is given by [5], n sin( θ B +θ1). sinθ = (1) B The gratings we employ are designed so that θ 1 is calculated for light in the middle of the visible spectrum, 500-nm wavelength. Using their measured blaze angle and equation 1, students calculate the index of refraction for their grating and compare this value to a value they obtain by measuring the index of refraction in the standard way; they shine a laser through the edge of the grating glass and measure angles for incident and refracted rays. CONCLUSIONS We have developed a series of nanotechnology modules that have been included in each quarter of our four-quarter introductory physics course sequence. In addition, we have included modified versions of these modules in our upper-level laboratories. Many of the modules involve interdisciplinary (for example engineering) applications that lend relevance to the experiments. These modules allow students to experience AFM applications at successive levels of complexity in their courses, so that by their senior level, they can operate the equipment at an advanced level, and develop useful skills transferable to their careers after graduation. ACKNOWLEDGMENTS Funding for this project was provided by the National Science Foundation Nanotechnology Undergraduate Education program, award #

11 REFERENCES 1. S. Tobias, D. E. Chubin, and K. Aylesworth, Rethinking Science as a Career: Perceptions and Realities in the Physical Sciences (Research Corporation, Tucson, AZ, 1995). 2. Boyer Commission on Educating Undergraduates in the Research University, Reinventing Undergraduate Education: A Blueprint for America's Research (State University of New York, Stony Brook, NY, 1998), 3. F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice-Hall, New Jersey, 1987), pp Microwave Optics System, Pasco Scientific, Foothills Blvd., Roseville, CA K. G. Vandervoort, S. L. Adams, and A. M. Hyder, Am. J. Phys., in press (2006). 6. K. C. Pohlmann, The Compact Disk Handbook (Middleton, WI, Eds. A-R, 1992).